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Part IV - RIAA compensation

In the concept development phase we explained our reasons to go with passive RIAA compensation. We are talking about passive filter circuit with a carefully tailored output characteristic. There is almost an infinite number of R, L and C combinations that can give us the required response. Two most common (and simplest) configurations are shown below.



Even though both circuits will perform well, there are some minute differences. Circuit "A" will have capacitors C1 and C2 working in series at the high end of the frequency bandwidth. That means that their parasitic inductances and resistances will add up. Everything else being equal, circuit "B" does not have that drawback, having only C1 connected directly across the filter's output and C2 in series with R2, making C2 parasitics negligible in comparison the required high value for R2. So, we will go with circuit "B".

COMPONENT VALUES

The filter circuit is really simple, indeed. Filter response is relatively easy to mathematically derive, however, equations in their closed form are pretty long (unlike those defining gain of the op-amp circuits). Luckily, should you decide to experiment with your own design, there are few good online calculators that work with pretty good.

Again, there is a large number of possible combinations (and online calculators make it easy to try many of them), but final choice will depend on circuits that are being connected at the input and output of the RIAA filter. Ideally, signals brough to the input should come from a source with a very low impedance. The filter's output should, ideally, be connected to an infinite impedance. Inevitable realities of practical circuits (non-zero input and non-infinity output impedance) will modify filter's response, it is our challenge to minimize the effects (or to qualify and compensate for them).

In our case,  the filter will see very low impedance the op-amp output (few ohms) and filter output will be connected to the op-amp input (few hundred million, or even a billion ohms). Selecting R1 value to be about thousand times higher than op-amp's output impedance is a good compromise between  filter accuracy and noise (high resistor values would help accuracy, but they will also have higher thermal noise, so it is on designer to pick his poison.... or how he mixes them).

Other than that, we need to be aware that calculations will give us results to few decimal points. Component vendors need to be more practical, though, so they make components with standardized values. We need to select and calculate values that are close to what is available on the market, or close to a combination of standard values (by adding components in series or parallel) and, if still not perfect, to understand and qualify effects.

Examining these effects, along with effects of component tolerances are the next steps we need to take.

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Starting with assumptions outlined above, we ended up with the following ideal filter:



Voltage source V10 is an ideal source with zero output resistance and RL2 is our load, which is going to be very high.

Resistor R10 and C20 came out right on the standard values, but R20 and C10 were a bit different. Let's see how practical considerations affect this circuit:



Our voltage source is less than perfect, with 50 ohm output impedance (by proper selection of op-amp we can go lower than that, for now let's play safe). R20 got replaced with two standard resistors connected in series and C10 became C1 with standard value of 220nF (0.22uF).

Now seems to be the right time to fire up the circuit simulation software and speed up our analysis.

Perfect RIAA has a perfect response, which is our reference:



We are examining very wide frequency range (10Hz-100kHz) just to make sure there are no surprises once we start looking at real-world imperfections.

Considering that we had to use standard component values instead of mathematically correct ones, we can expect that there will be deviation in the RIAA response. We expect (hope?) differences to be very small. The picture below shows deviation of the practical circuit from the ideal RIAA curve:



Assuming standardized component values, maximum deviation from the perfect RIAA curve will be 0.07dB at about 200Hz. Looks pretty good, doesn't it? Our wish list had the accuracy within 0.2dB, looks like our wishes are coming true!!!!

So let's call it a day and declare victory!

Well.....not so fast..... I don't feel like exercising my marketing skills at this time, there is more work to be done....

[Audiovista]

All right, so maximum nominal deviation from ideal RIAA characteristic is only 0.07dB. Life is good! And would be much better were there no component tolerances.

Let's take a quick look now at how component tolerances affect this characteristic. In a typical RIAA preamplifier you may see that "high precision 1% resistors and 5% capacitors" are used. And yes, indeed, compared to 5 or 10% resistors and 10-20% accurate capacitors, this is much better. Thanks to our simulation software it is relatively easy to analyze possible distribution of the deviation by using Monte Carlo analysis (http://en.wikipedia.org/wiki/Monte_Carlo_analysis). By entering analysis parameters (in this case twenty pseudo-random scenarios - we can go up to 400 combinations, but the graph would be too busy to be illustrative), the software calculates RIAA tracking error by varying R and C values within allowed tolerance.

Picture below shows results for 1% resistors and 5% capacitors.



Now, the maximum deviation comes to be over 0.4dB (at 10kHz and above). Still a good result, but far cry from nominal 0.07dB. And we're not done yet!

Smart software designers provided an easy way for us to calculate what will happen when cards stack against us - The Worst Case Analysis will show results when tolerances of the filter components stack up to give us maximum error. And the new graph is as follows:



And what did just happen? Our nice number of 0.07dB (upper trace) became much larger 0.54dB (at 10kHz)!

How does all of this affect you? Well, say there is a RIAA preamp that uses 1% accurate resistors and 5% capacitors. And let's assume that it is not an extremely expensive unit where you pay many $$$ for component selection on $$$ instrument (please note that regular digital multimeter with capacitance range is not likely to give you good enough results). A crafty marketing expert may advertise such a preamp as having "better than 0.1dB RIAA tracking accuracy". In fact, you particular preamplifier may have deviation from perfect RIAA anywhere between 0dB (no deviation - congratulations, you lucked out!) and 0.54dB (worst case). More typically, as Monte Carlo analysis suggests, you are likely to have a preamp with accuracy within 0.4dB.

We already decided that we will not call it 0.07dB (otherwise I would have stopped on the previous post and saved few hours of analysis). But 0.54dB is just too much for me to take, and I certainly do not want to give up on a noble goal of reaching below 0.2dB.

More work is coming....

[Audiovista]

Measuring every single capacitor and resistor to find perfect match is not an option - the preamp would just cost way too much.

Let's take a look at the lowest tolerance components out there. After a short search we uncover 0.1% resistors with adequate values. That's a good step forward. Now the trickier part - capacitors.... 2% tolerance can be found, which is pretty good, considering all the factors affecting the tolerance in production. But, there is also a 1% capacitor, right value and right type. Unfortunately, this is soon to be NOS, considering that manufacturer announced that this type will be discontinued. Oh well, for now we'll just buy as many as we can and will keep searching for a current production before we're out of stock.

Now, we have 0.1% resistors and 1% capacitors. Let's re-run Monte Carlo analysis:



Deviation from an ideal RIAA is now less than 0.12dB, definitely much better than 0.4dB in previous case. That would be our typical number. Worst case analysis is illustrated below:



Upper line is our nominal curve and lower trace a maximum deviation (worst case) which is just below 0.15dB (previously 0.54dB).

At this point we can comfortably rest, the worst case becomes our spec and it meets initially set requirements for a RIAA tracking accuracy.

In conclusion - RIAA tracking is very sensitive to component values. Even decent components (1% resistors and 5% capacitors) may result in deviation more than 600% above nominal, and "as good as they get" parts (0.1% resistors and 1% capacitors) yield worst case deviation of over 100% above nominal.

Careful design and understanding of necessary tradeoffs gives us good starting values and low nominal deviation. Thorough analysis supported by powerful software helps us understand effects of real, imperfect components and search for optimum solution within predefined goals.

We are ready now to start wrapping up the schematics and move on with the design.